MATLAB Implementation of Waveguide Computation Using the Transfer Matrix Method

The transfer matrix method serves as a fundamental numerical technique in waveguide computations, particularly effective for analyzing electromagnetic properties of multilayer dielectric structures. This approach decomposes complex waveguide problems into simpler individual layers and utilizes matrix operations to solve overall transmission characteristics. In MATLAB implementation, the core workflow of the transfer matrix method involves several key steps: 1. Define material parameters for each dielectric layer, including permittivity (ε) and permeability (μ), which determine electromagnetic wave propagation characteristics per layer. This can be implemented through parameter arrays or structure arrays in MATLAB. 2. Establish field quantity relationships between adjacent layers based on boundary conditions, typically using continuity conditions for electric and magnetic fields. MATLAB's matrix operations efficiently handle these boundary condition equations. 3. Construct the transfer matrix for each layer, describing phase changes and impedance matching as electromagnetic waves propagate through the layer. The transfer matrix can be computed using MATLAB's matrix exponentiation functions for homogeneous layers. 4. For multilayer structures, sequentially multiply all layer transfer matrices to obtain the overall system transfer matrix. MATLAB's matrix multiplication capabilities (using the * operator or mtimes function) enable efficient cascading of multiple layers. 5. Solve for reflection and transmission coefficients through boundary conditions relationships (e.g., incident and reflected wave relations). This typically involves solving linear equations using MATLAB's backslash operator (\) or linsolve function. The method's advantages include high computational efficiency, particularly suitable for periodic structures or gradient-index waveguides. MATLAB's built-in matrix operations allow rapid implementation with capabilities for parameter scanning and optimization design using loops and optimization toolbox functions. Practical extensions of this method may incorporate loss analysis through complex-valued material parameters or nonlinear effects using iterative solving techniques. By adjusting layer counts and parameters, the code can simulate various waveguide structures including photonic crystal waveguides and plasmonic waveguides through appropriate material parameter definitions.